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Open-Closed Moduli Spaces and Related Algebraic Structures

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Abstract

We set up a Batalin–Vilkovisky Quantum Master Equation (QME) for open-closed string theory and show that the corresponding moduli spaces give rise to a solution, a generating function for their fundamental chains. The equation encodes the topological structure of the compactification of the moduli space of bordered Riemann surfaces. The moduli spaces of bordered J-holomorphic curves are expected to satisfy the same equation, and from this viewpoint, our paper treats the case of the target space equal to a point. We also introduce the notion of a symmetric Open-Closed Topological Conformal Field Theory (OC TCFT) and study the L ∞ and A ∞ algebraic structures associated to it.

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Authors and Affiliations

  1. Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794, USA

    Eric Harrelson

  2. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Alexander A. Voronov

  3. Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN, 47907-2067, USA

    J. Javier Zúñiga

Authors
  1. Eric Harrelson
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  2. Alexander A. Voronov
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  3. J. Javier Zúñiga
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Correspondence to Alexander A. Voronov.

Additional information

Partially supported by NSF and JSPS grants and a University of Minnesota Doctoral Dissertation Fellowship.

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Harrelson, E., Voronov, A.A. & Zúñiga, J.J. Open-Closed Moduli Spaces and Related Algebraic Structures. Lett Math Phys 94, 1–26 (2010). https://doi.org/10.1007/s11005-010-0418-0

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  • DOI: https://doi.org/10.1007/s11005-010-0418-0

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